Recent studies of the properties of phospholipid dispersions in water indicate that a higher-order phase transition occurs involving a spontaneous transformation from a unilamellar liquid-crystal state to a suspension of large, unilamellar vesicles upon increasing the ambient temperature; it has been suggested that the unilamellar vesicles that form are a critical state. The thermodynamic properties of this transformation have been inferred primarily from the properties of air-water surface films in equilibrium with the dispersed phospholipid phase. A more direct, and conceptually simpler, analysis of the thermodynamic properties of this higher-order transition may be attained by measurements of the temperature dependence of the heat capacity of the lipid dispersions. Since transformations of this type are believed to be intimately involved in the assembly of cell membranes, we have developed an extremely sensitive differential heat conduction calorimeter for measuring heat capacities of aqueous membrane lipid dispersions. (It should be noted that attempts to measure this transformation in commercial calorimeters have not been successful.) This instrument has certain obvious advantages over the commercial differential scanning calorimeters, notably baseline repeatability and resolution. In this transformation, to measure the heat capacity change sensibly requires a calorimeter with a sensitivity of 0.0001 cal/deg-g. We estimated the sensitivity for the energetics of unilamellar vesicle formation from multilamellar liquid crystals using the intrabilayer cohesive energy of approximately 0.01 ergs/cm2. Assuming a one-degree temperature interval for the transition, this translates into a change of heat capacity on the order of 0.001 cal/deg-g. To assure reasonable precision, we required an instrument with a sensitivity of at least one percent of the calculated transition energy. Moreover, since only mg quantities of membrane lipids are available, we are restricted to small sample sizes (1 cc).